AN ACR B757 HAD AN NMAC WITH A SHORTS 360 IN THE MIA TFC PATTERN. THE SHORTS AND THE B757 EACH HAD ENCOUNTERS WITH OTHER ACFT BEFORE THEY GOT ON THE GND. WX FACTORS SCUD AND RAIN SHOWERS ON THE ILS COURSES AND GENERALLY AT ALL ALTS IN THE TFC PATTERN.

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ON FINAL APCH RWY 9R MIA. AT APPROX 500 FT AGL; TWR COMMANDED AN IMMEDIATE PULL UP AND GAR WITH AN IMMEDIATE R TURN TO HDG 180 DEGS UP TO 3000 FT MSL. WE WERE ADVISED THAT A SHORTS TWIN ENG ACFT HAD STRAYED INTO OUR ILS COURSE PATH. RADAR VECTORS WERE PROVIDED TO RETURN US TO THE ILS FOR RWY 9R AGAIN. RADAR GAVE US OUR FINAL INTERCEPT HDG; WHICH WAS 360 DEGS. AS WE BROKE OUT OF THE CLOUDS PRIOR TO LOC CAPTURE; WE WERE LOOKING AT A B727 ACFT AT 12 O'CLOCK ON THE ILS TO RWY 9L AT OUR SAME ALT. COURSE CAPTURE AND ALIGNMENT TO ILS; RWY 9R REQUIRED A RAPID TURN AT A BANK ANGLE OF 50 DEGS TO PREVENT A SEVERE OVERRUN OF THE ILS AND ANOTHER CLOSE ENCOUNTER WITH AN ACFT ON THE PARALLEL APCH. NO HDOF FROM APCH CTL TO TWR WAS EVER RECEIVED. MY FULL ATTN WAS ON THE OTHER ACFT AND COMPLETING ALL NECESSARY CHKLISTS AND I DID NOT CONTACT TWR FOR LNDG CLRNC. AFTER TELEPHONING THE MIA TWR SUPVR; HE STATED THAT PART OF THE ARPT WAS VFR AND PART IFR AND THAT THE COMMUTER ACFT DRIFTED INTO OUR IFR AIRSPACE AS HE WAS LNDG VFR AT THE N SIDE OF THE ARPT. THE ACFT NEVER APPEARED ON TCASII NOR DID EITHER ONE OF US SEE THE ACFT IN QUESTION. I WOULD SUGGEST THAT NO VFR APCHS AND LNDGS BE CONDUCTED WHEN THE ARPT IS EVEN PARTIALLY IFR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAYS THAT 'THE CHAIN WAS GETTING LONGER' AND MIA WAS APPARENTLY TRYING TO SHORTEN THINGS UP. THE RPTR WAS 'IN AND OUT OF SCUD' FOR RWY 9L. THE RPTR CALLED ZMA AND FOUND THAT TRAINING WAS IN PROGRESS AND THE N HALF OF THE FIELD WAS VMC; THE S HALF IMC. THE RPTR ADMITTED THAT HE GOT 'A LITTLE BIT TESTY WITH THE TWR' BOTH ON THE GND; IN THE AIR; AND ON THE TELEPHONE. THE RPTR HAS A HARD TIME UNDERSTANDING HOW AN ARPT CAN BE HALF IMC; HALF VMC. VISUAL APCHS WERE BEING MADE TO RWYS 9R AND 12 WHILE IFR APCHS WERE BEING MADE TO RWY 9L. SUPPLEMENTAL INFO FROM ACN 339768: OPS CALLED US TO REPOS THE ACFT INTO MIAMI. ACFT WAS VFR ONLY AND PRESSURIZATION WAS INOP/MEL'ED. WE MAINTAINED VFR BY DEVIATING AROUND SMALL BUILD-UPS AND LIGHT RAIN SHOWERS. WE WERE TOLD TO EXPECT RWY 12; THE CAPT PUT IN A REQUEST FOR RWY 9L. APCH CTLR THEN ADVISED US THAT WE HAVE TFC AT OUR 12-1 O'CLOCK; OPPOSITE DIRECTION; WILL BE TURNING BEHIND US FOR RWY 12. ONCE THE CAPT CALLED TFC IN SIGHT; APCH CTL CLRED US FOR THE VISUAL RWY 9L. CTLR CLRED US TO LAND RWY 9L. WE TURNED TO A HDG OF 150 DEGS TO AVOID ENTERING IMC AND RAIN. AS I'M TURNING; I SAW OUT THE R WINDOW A B757 POP OUT OF THE CLOUDS ON THE SAME APCH ABOUT 50-100 FT BELOW US. WE INITIATED A MISSED APCH. IN THE PROCESS; WE CROSSED THE APCH PATH OF RWY 9R AND CAUSED ANOTHER B757 TO GO MISSED APCH. WE VECTORED AROUND THE AREA AND I LANDED UNEVENTFULLY ON RWY 9R. APCH/TWR NEVER ISSUED A TA OF THE B757 ON THE SAME APCH 100 FT BELOW US. FACTORS FOCUSED ON APCH/TWR FAILING TO POINT OUT TFC ON APCH FOR THE SAME RWY AND OUR MISSED APCH; NOT FLYING RWY HDG AS THE PUBLISHED PROC CALLS FOR.